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Publications of the Computational Algebra Research Group

1. Murray SH. Representations of parabolic and Borel subgroups, (2006), preprint
2. Cohen AM, Haller S, Murray SH. Computing in unipotent and reductive algebraic groups, (2006), preprint
3. Cohen AM, Knopper JW, Murray SH. Automatic proof of graph nonisomorphism, (2008), preprint
4. Cohen AM, Murray SH. Algorithm for Lang's Theorem, (2008), preprint
5. Murray SH, Roney-Dougal CM. The spinor norm and homomorphism algorithms for classical groups, (2008), preprint
6. Murray SH, Nguyen MVM. Enumeration of strength 3 mixed orthogonal arrays, (2008), preprint
7. Cohen AM, Murray SH. An automated proof theory approach to computation with permutation groups, (2008), preprint
8. Cooperman G, Murray SH. Computable subgroup chains and shadowing, (2008), preprint
9. Murray SH, Saunders N. Magma Proof of Strict Inequalities for Minimal Degrees of Finite Groups, (2009), preprint
10. Cohen AM, Murray SH. An algorithm for Lang's theorem, Journal of Algebra, 322 (2009), no. 3, 675.
11. Nebe G, Steel A. Recognition of division algebras, Journal of Algebra, 322 (2009), 903–909.
12. Fieker C. Minimizing representations over number fields II: Computations in the Brauer group, Journal of Algebra, 322 (2009), 752–763.
13. Belabas K, Hoeij M, Kluners J, Steel A. Factoring polynomials over global fields, Journal de th'eorie des nombres de Bordeaux, 21 (2009), no. 1, 15–39.
14. An J, Cannon JJ, O'Brien EA, Unger WR. The Alperin weight conjecture and Dade's conjecture for the simple group Fi24', LMS Journal of computation and mathematics, 11 (2008), 100–145. MR2410917
15. Pujol X, Stehle D. Rigorous and efficient short lattice vectors enumeration, Advances in Cryptology – Asiacrypt 2008, Asiacrypt 2008, Lynn Batten (ed.), LNCS, Springer, Berlin, (2008), 0000.
16. Cohen AM, Haller S, Murray SH. Computing in unipotent and reductive algebraic groups, LMS Journal of Computational Mathematics, 11 (2008), 343–366. MR2452553
17. Akhavi A, Stehle D. Speeding-up Lattice Reduction with Random Projections, LATIN 2008, LATIN 2008, E. Laber (ed.), LNCS, Springer, New York, (2008), 293–305.
18. Fieker C, Pohst ME. A lower regulator bound for number fields, Journal of Number Theory, 128 (2008), 2767–2775. MR2441075
19. Fieker C, Klueners J. Galoisgruppen in Magma, Computeralgebra Rundbrief, 43 (2008), 11–12.
20. Dembélé L, Donnelly S. Computing Hilbert Modular Forms over Fields with Nontrivial Class Group, Lecture Notes in Computer Science, 5011 (2008), 371–386. MR2467859
21. Cannon JJ, Holt DF. The transitive permutation groups of degree 32, Experimental Mathematics, 17 (2008), no. 3, 307–314. MR2455702
22. Murray SH. Representations of parabolic and Borel subgroups, Communications in Algebra, 35 (2007), no. 2, 455–459. MR2294610
23. Fieker C, Graaf W. Finding integral linear dependencies of algebraic numbers and algebraic Lie algebras, London Mathematical Society Journal of Computational Mathematics, 10 (2007), 271–287.
24. Fieker C. Sparse representation for cyclotomic fields, Experimental Mathematics, 16 (2008), no. 4, 493–500.
25. Unger WR. Computing the soluble radical of a permutation group, Journal of Algebra, 300 (2006), no. 1, 305–315. MR2228650
26. Cannon JJ, Holt DF. Computing conjugacy class representatives in permutation groups, Journal of Algebra, 300 (2006), no. 1, 213–222. MR2228644
27. Fieker C, Pohst ME. Dependency of units in number fields, Mathematics of Computation, 75 (2006), no. 255, 1507–1518. MR2219041
28. Unger WR. Computing the character table of a finite group, Journal of Symbolic Computation, 41 (2006), no. 8, 847–862. MR2246713
29. Voight J. Computing CM points on Shimura curves arising from cocompact arithmetic triangel groups, Algorithmic Number Theory: ANTS-VII, 7th International Symposium, ANTS-VII, Florian Hess, Sebastian Pauli, Michael Post (eds.), Lecture Notes in Computer Science, 4076 Springer-Verlag, Berlin, (2006), 406–420. ISBN 3-540-36075-1 MR2282939
30. Stehle D. On the randomness of bits generated by sufficiently smooth functions, Algorithmic Number Theory: ANTS-VII, 7th International Symposium, ANTS-VII, Florian Hess, Sebastian Pauli, Michael Post (eds.), Lecture Notes in Computer Science, 4076 Springer-Verlag, Berlin, (2006), 257–274. ISBN 3-540-36075-1 MR2282929
31. Harrison M, Schicho J. Rational parametrisation for degree 6 del pezzo surfaces using Lie algebras, Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation: ISSAC ' 06, ISSAC '06: International symposium on symbolic and algebraic computation, Jean-Guillaume Dumas (ed.), Symbolic and Algebraic Computation, ACM, New York, (2006), 132–137. ISBN 1-59593-276-3 MR2289111
32. Fieker C. Applications of the class field theory of global fields, Discovering Mathematics with Magma. Reducing the Abstract to the Concrete, Algorithms and Computation in Mathematics, Springer, Berlin, (2006), 31–62. ISBN 3-540-37632-1 MR2278922
33. Roney-Dougal CM, Unger WR. Computing the primitive permutation groups of degree less than 1000, Discovering Mathematics with Magma. Reducing the Abstract to the Concrete, Algorithms and Computation in Mathematics, Springer, Berlin, (2006), 243–260. ISBN 3-540-37632-1 MR2278931
34. Steel A. Conquering inseparability: primary decomposition and multivariate factorization over algebraic function fields of positive characteristic, Journal of Symbolic Computation, 40 (2005), no. 3, 1053–1075. MR2167699
35. Cannon JJ, Holt DF, Slattery M, Steel A. Computing subgroups of bounded index in a finite group, Journal of Symbolic Computation, 40 (2005), no. 2, 1013–1022. MR2167681
36. Cohen A, Murray SH, Taylor DE. Computing in groups of Lie type, Mathematics of Computation, 73 (2004), 1477–1498. MR2047097
37. Fieker C. Minimizing representations over number fields, Journal of Symbolic Computation, 38 (2004), 833–842. MR2094558
38. Cannon JJ, Holt DF. Computing maximal subgroups of finite groups, Journal of Symbolic Computation, 37 (2004), 589–609. MR2094616
39. Steel A, Ramnarine KV, Criton A, Davidson F, Allan PL, Humphries N, Routh HF, Fish PJ, Hoskins PR. Angle-dependence and reproducibility of dual-beam vector Doppler ultrasound in the common carotid arteries of normal volunteers, Ultrasound in Medicine and Biology, 94 (2004), 271–276.
40. Cannon JJ, Eick B, Leedham-Green CR. Special polycyclic generating sequences for finite soluble groups, Journal of Symbolic Computation, 38 (2004), no. 5, 1445–1460. MR2168723
41. Roney-Dougal CM, Unger WR. The affine primitive permutation groups of degree less than 1000, Journal of Symbolic Computation, 35 (2003), 421–439. 2004e:20002
42. Fieker C, Kluners J. Minimal discriminants for fields with small Frobenius groups as Galois groups, Journal of Number Theory, 99 (2003), 318–337. 2004f:11147
43. Cannon JJ, Holt D. Automorphism group computation and isomorphism testing in finite groups, Journal of Symbolic Computation, 35 (2003), 241–267. 2004c:20035
44. Cohen A, Murray SH, Pollet M, Sorge V. Certifying solutions to permutation group problems, Automated Deduction, CADE-19, F. Baader (ed.), Lecture Notes in Artificial Intelligence, Springer, Berlin, (2003), 257–273. ISBN 3-540-40559-3
45. Holmes PE, Linton SA, Murray SH. Product replacement in the Monster group, Experimental Mathematics, 12 (2003), no. 1, 123–126. 2003h:20003
46. Fieker C. Ueber Magma, Computeralgebra Rundbrief, 32 (2003), 12–13.
47. Steel A. A new scheme for computing with algebraically closed fields, ANTS-V Proceedings, 5th International Symposium, ANTS-V, Claus Fieker, David R Kohel (eds.), Lecture Notes in Computer Science, Springer, Berlin Heidelberg, (2002), 491–505. ISBN 3-540-43863-7 MR2041106
48. Fieker C, Kohel DR. ANTS-V Proceedings, Lecture Notes in Computer Science, Springer, Berlin Heidelberg, (2002), 515.
49. Cannon JJ, Unger WR. Magma, Handbook of Computer Algebra, foundations, applications, systems, Springer, Berlin, (2002), –.
50. Leedham-Green CR, Murray SH. Variants of product replacement, Computational and statistical group theory, Statistical methods in group theory, Robert Gilman, Vladimir Shpilrain, Alexei G. Myasnikov (eds.), Contemporary Mathematics, American Mathematical Society, Providence, (2002), 97–104. MR1929718
51. Combe D, Palmer WD, Unger WR. Bhaskar Rao designs and the alternating group A4, Australasian Journal of Combinatorics, 24 (2001), 275–283. 2002f:05027
52. Cannon JJ, Cox BC, Holt DF. Computing the subgroups of a permutation group, Computational Algebra and Number Theory, 31 (2001), 149–161. 2002e:20008
53. Fieker C. Computing class fields via the Artin map, Mathematics of Computation, 70 (2001), 1293–1303. MR1826583
54. Murray SH. Conjugacy classes in maximal parabolic subgroups of general linear groups, Journal of Algebra, 233 (2000), 135–155. 2002f:20069
55. Fieker C, Friedrichs C. On reconstruction of algebraic numbers, Algorithmic Number Theory, 4th International Symposium, ANTS-IV, Wieb Bosma (ed.), Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg, (2000), 285 – 296. ISBN 3 540 67695 3 2002g:11181
56. Kemper G, Steel A. Some algorithms in invariant theory of finite groups, Computational Methods for Representations of Groups and Algebras, Progress in Mathematics, 173 Birkhauser Verlag, Basel, Switzerland, (1999), 267–285. ISBN 3-7643-6063-1 2000j:13009
57. Kemper G, Steel A. Some algorithms in invariant theory of finite groups, Progress in Mathematics, 173 (1998), 267–285. 2000j:13009
58. Bosma W, Cannon JJ, Steel A. Lattices of compatibility embedded finite fields, Journal of Symbolic Computation, 24 (1997), no. 3/4, 351–369. 99a:11143
59. Bosma W, Cannon JJ, Playoust CE. The magma algebra system I: the user language, Journal of Symbolic Computation, 24 (1997), no. 3/4, 235–265. MR1484478
60. Cannon JJ, Playoust CE. Using the magma computer algebra system in abstract algebra courses, Journal of Symbolic Computation, 23 (1997), no. 5/6, 459–484.
61. Cannon JJ, Holt DF. Computing chief series, composition series and socles in large permutation groups, Journal of Symbolic Computation, 24 (1997), no. 3/4, 285–301. 98m:20009
62. Cannon JJ, Cox BC, Holt DF. Computing Sylow subgroups in permutation groups, Journal of Symbolic Computation, 24 (1997), no. 3/4, 303–316. 98m:20010
63. Steel A. A new algorithm for the computation of canonical forms of matrices over fields, Journal of Symbolic Computation, 24 (1997), no. 3/4, 409–432. 98m:65070
64. Cannon JJ, Souvignier B. An the computation of conjugacy classes in permutation groups, Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, ISSAC 97, Wolfgang W. Kuchlin (ed.), ISSAC 97, ACM Press (Association for Computing Machinery, Inc.), New York, U.S.A, (1997), 392–399. ISBN 0 89791 875 4 MR1810005
65. Cannon JJ, Playoust CE. Magma: a new computer algebra system, Euromath Bulletin, 2 (1996), 113–144. MR1413180
66. Bailey G. Xvoigt: An interactive absorption line fitting program for the X window system, Publications of the Astronomical Society of Australia, 12 CSIRO Publications, Melbourne, (1995), 239–243.
67. Celler F, Leedham-Green CR, Murray SH, Niemeyer AC, O'Brien EA. Generating random elements of a finite group, Communications in Algebra, 23 (1995), no. 13, 4931–4948. MR1356111
68. Murray SH, O'Brien EA. Selecting base points for the Schreier-Sims algorithm for matrix groups, Journal of Symbolic Computation, 19 (1995), no. 6, 577–584. MR1370623
69. Butler G, Cannon JJ. On Holt's algorithm, Journal of Symbolic Computation, 15 (1993), MR1281200
70. Bosma W, Cannon JJ. A Handbook of Cayley Functions, 1st edn (1991), 1–243.
71. Butler G, Cannon JJ. Computing Sylow subgroups of permutation groups via homomorphic images of centralizers, Journal of Symbolic Computation, 12 (1991), 443–458. 92m:20002
72. Cameron PJ, Cannon JJ. Recognizing doubly transitive groups, Journal of Symbolic Computation, 12 (1991), 459–474. 92m:20003
73. Butler G, Cannon JJ. The design of Cayley — a language for modern algebra, Design and Implementation of Symbolic Computation Systems, Miola A (ed.), Lecture Notes in Computer Science, 429 Springer, (1990), 10–19.
74. Butler G, Cannon JJ. Computing in permutation and matrix groups III : Sylow subgroups, Journal of Symbolic Computation, 8 (1989), 241–252. 90i:20003
75. Butler G, Cannon JJ. Cayley version 4: The user language, Proceedings of the 1988 International Symposium on Symbolic and Algebraic Computation, International Symposium on Symbolic and Algebraic Computation, Rome, July 4–8, 1988, Gianni P (ed) (ed.), Lecture Notes in Computer Science, 358 (1988), MR1053754
76. Butler G, Cannon JJ. The design of Cayley — A language for modern algebra, Proceedings of the ACM SIGPLAN 88 Conference on Programming Language Design. Atlanta, Georgia, (1988), MR1053754
77. Unger WR, Wehrhahn KH. Species of ordered partitions, Ars Combinatoria, 21-A (1986), 141–146. 87j:05018
78. Cannon JJ, Richardson JS. Cayley — Teaching Group Theory by Computer, SIGSAM Bulletin, 18 (1984), 15–18.
79. Cannon JJ. An introduction to the group theory language Cayley, Computational Group Theory, Atkinson MD (ed.), Academic Press, London, (1984), 145–183. MR0760656
80. Cannon JJ. A computational toolkit for finite permutation groups, Proceedings of the Rutgers Group Theory Year, 1983 - 1984, Aschbacher M et al (ed.), CUP, New York, (1984), 1–18.
81. Butler G, Cannon JJ. Computing with permutation and matrix groups I: Normal closure, commutator subgroups, series, Mathematics of Computation, 39 (1982), 671–680.
82. Cannon JJ. The basis of a computer system for modern algebra, Proceedings of the 1981 ACM Symposium on Symbolic and Algebraic Computation, Snowbird, Utah, August, 1981, SYMSAC '81, Assoc. Comp. Mach., New York, (1981), 1–5.
83. Cannon JJ. Effective procedures for the recognition of primitive groups, Proceedings of Symposia in Pure Mathematics, 37 (1980), 487–493. MR0604626
84. Cannon JJ. Software tools for group theory, Proceedings of Symposia in Pure Mathematics, 37 (1980), 495–502. MR0604627
85. Cannon JJ, McKay J, Young. Presentations for simple groups of order less than 105, Communications in Algebra, 7 (1979), 1397–1406. 80e:20023
86. Cannon JJ. A draft description of the group theory language Cayley, Proceedings of the 1976 ACM Symposium on Symbolic and Algebraic Computation, Yorktown Heights, N.Y., August 1976, Jenks RD (ed.), Assoc. Comp. Mach., New York, (1976), 66–84.
87. Cannon JJ. On the teaching of mathematics for the social sciences, Proceedings of a Conference on Mathematics needed for Particular Social Sciences, Canberra, May 1974, Australian Academy of Social Sciences, (1976), 228–237.
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